Finite Group Databasebeta

← #25966385

Subgroups — #25966385

Order 11008.

1998 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147891C212yesmaximal, complemented
2#19145201C218yesmaximal, complemented
3#19145190C218yesmaximal, complemented
4#19145119C211yesmaximal, characteristic, complemented
5#19145041C211yesmaximal, characteristic, complemented
6#19144941C212yesmaximal, complemented
7#19144204C214yesmaximal, complemented
8C4×#13063347C214yesmaximal, complemented
9C2×C4×M16×C43C211yesmaximal, characteristic, complemented
10C2×#13063347C2214yes—
11#14583456C2214yes—
12#14583456C2212yes—
13#14583449C2212yes—
14#14583449C2214yes—
15#14583433—24no—
16#14583433—24no—
17#14583433C2218yes—
18#14583410—24no—
19#14583410C2214yes—
20C4×#10621898—24no—
21C4×#10621898C2214yes—
22#14583308C2218yescomplemented
23#14583293C2214yescomplemented
24#14583288C2214yescomplemented
25#14583268C2214yescomplemented
26#14583264C2214yescomplemented
27#14583259C2218yescomplemented
28#14583157C2218yes—
29#14583152C2218yes—
30#14583145C22116yes—
31C4×Dic172C2218yescomplemented
32C4×#10621873C22116yescomplemented
33C4×D344C2218yescomplemented
34#14582937C2214yes—
35#14582896C2218yes—
36C22×M16×C43C2212yes—
37C22×C42×C43C2211yescharacteristic
38C4×M16×C43C2218yes—
39C2×#97×C43C2211yescharacteristic
40C2×#97×C43C2211yescharacteristic
41C2×C4×C8×C43C2212yes—
42C2×#10621898—24no—
43C2×#10621898C2314yes—
44#13063347—216no—
45C2×Dic172C2314yes—
46C2×#10621873C2318yes—
47C2×D344C2314yes—
48#13063325C2312yes—
49#13063325C2314yes—
50#13063322C2312yes—
51#13063319—28no—
52#13063317—24no—
53#13063317C2314yes—
54#13063313—24no—
55#13063313C2314yes—
56#13063308—28no—
57#13063308—24no—
58#13063304—24no—
59#13063304—24no—
60#13063304C2318yes—
61#13063299—24no—
62#13063299—24no—
63#13063299C2318yes—
64#13063294—24no—
65C4×Dic86—24no—
66C4×Dic86—24no—
67C4×Dic86C2318yes—
68C4×D172—24no—
69C4×D172—24no—
70C4×D172C2318yes—
71C4×C22⋊D43—28no—
72C4×C22⋊D43—28no—
73C4×C22⋊D43—28no—
74#13063284—24no—
75#13063284C2314yes—
76#13063282—28no—
77#13063282—24no—
78C42×D43—24no—
79#13063259C2318yes—
80#13063257C2318yes—
81#13063250C23116yes—
82#13063247C23116yes—
83C23×C4×C43D412yes—
84C23×C4×C43C2311yescharacteristic
85C2×M16×C43—28no—
86C2×M16×C43C2318yes—
87C22×C8×C43C2312yes—
88C22×C8×C43C2312yes—
89C2×C42×C43D412yes—
90C2×C42×C43D412yes—
91C2×C42×C43D412yes—
92C2×C42×C43C2311yescharacteristic
93C2×C42×C43C2314yes—
94C2×C42×C43C2311yescharacteristic
95#97×C43C2314yes—
96#97×C43C2314yes—
97C4×C8×C43C2318yes—
98C24×C43C2×D411yescharacteristic
99C22×C4×C43—24no—
100C22×C4×C43—44no—
101C22×C4×C43C2×D412yes—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D414yes—
104C22×C4×C43C2×D412yes—
105C22×C4×C43C2×D412yes—
106C22×C4×C43C2×D414yes—
107C22×C4×C43C2412yes—
108C22×C4×C43C2411yescharacteristic
109C2×C22⋊D43—24no—
110C2×C22⋊D43—28no—
111#10621898—216no—
112#10621898—416no—
113C2×D172—24no—
114C2×D172C2414yes—
115C2×C4×D43—24no—
116C2×C4×D43—28no—
117C2×Dic86—24no—
118C2×Dic86C2414yes—
119M16×C43—216no—
120C2×C8×C43—24no—
121C2×C8×C43#4118yescomplemented
122C2×C8×C43C2414yes—
123C2×C8×C43C2414yes—
124C42×C43C2×D411yescharacteristic
125C42×C43C2×D414yes—
126C42×C43C2×D412yes—
127C42×C43C2×D414yes—
128C42×C43C2×D411yescharacteristic
129C42×C43C2412yes—
130C42×C43C2412yes—
131C22⋊Dic43—28no—
132C22⋊Dic43—24no—
133(C2×D43)⋊C4—28no—
134(C2×D43)⋊C4—28no—
135(C2×D43)⋊C4—28no—
136C4⋊Dic43—24no—
137C4⋊Dic43—24no—
138C4⋊Dic43C2418yes—
139Dic43⋊C4—28no—
140Dic43⋊C4—28no—
141Dic43⋊C4—28no—
142C4×Dic43—28no—
143C4×Dic43—24no—
144Dic172—28no—
145D344—28no—
146#10621873—216no—
147C23×C43—22no—
148C23×C43—42no—
149C23×C43C22×D412yes—
150C23×C43C22×D411yescharacteristic
151C22×D43—24no—
152C2×C4×C43—22no—
153C2×C4×C43—24no—
154C2×C4×C43—28no—
155C2×C4×C43—24no—
156C2×C4×C43—24no—
157C2×C4×C43—42no—
158C2×C4×C43—44no—
159C2×C4×C43C22×D412yes—
160C2×C4×C43C22×D412yes—
161C2×C4×C43C22×D414yes—
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C22×D412yes—
164C2×C4×C43C2×#4114yes—
165C2×C4×C43C2511yescharacteristic
166C22⋊D43—416no—
167C22⋊D43—48no—
168C2×Dic43—24no—
169C2×Dic43—28no—
170D172—28no—
171D172—48no—
172C4×D43—48no—
173C4×D43—416no—
174Dic86—28no—
175Dic86—48no—
176C8×C43—24no—
177C8×C43C2×#4118yes—
178#60676—431nomaximal, Sylow
179C22×C43—22no—
180C22×C43—22no—
181C22×C43—24no—
182C22×C43—44no—
183C22×C43#53212yes—
184C22×C43C23×D411yescharacteristic
185C2×D43—44no—
186C2×D43—48no—
187C4×C43—22no—
188C4×C43—24no—
189C4×C43—22no—
190C4×C43#53212yes—
191C4×C43#57514yes—
192C4×C43C22×#4112yes—
193Dic43—44no—
194Dic43—48no—
195#3444—432no—
196#3172—438no—
197#3171—438no—
198#3162—431no—
199#3150—431no—
200#3135—432no—
201#3054—434no—
202C4×#135—434no—
203C2×C4×M16D4311yescharacteristic, complemented
204C2×C43—22no—
205C2×C43—42no—
206C2×C43C2×#53211yescharacteristic
207C2×C43C2×#57512yes—
208D43—84no—
209C2×#135—434no—
210C22×M16C2×D4312yes—
211#533—432no—
212#533—434no—
213#532—434no—
214#532—432no—
215#529—438no—
216#529—864no—
217#529—864no—
218#525—434no—
219#525—864no—
220C4×#41—434no—
221C4×#41—864no—
222C22×C42C2×D4311yescharacteristic
223#501—438no—
224#497—434no—
225#496—434no—
226#491—434no—
227#490—434no—
228#489—438no—
229#470—438no—
230#469—438no—
231#468—4316no—
232C4×Q16—438no—
233C4×SD16—4316no—
234C4×D8—438no—
235#427—434no—
236#416—438no—
237C4×M16C2×D4318yes—
238C2×#97C2×D4311yescharacteristic
239C2×#97C2×D4311yescharacteristic
240C2×C4×C8C2×D4312yes—
241C43#6067611yescharacteristic, complemented, Sylow
242C2×#41—434no—
243C2×#41—864no—
244C23×C4D17212yes—
245C23×C4C22×D4311yescharacteristic
246#135—8616no—
247C2×Q16—434no—
248C2×SD16—438no—
249C2×D8—434no—
250C2×M16—28no—
251C2×M16C22×D4318yes—
252C22×C8C22×D4312yes—
253C22×C8C22×D4312yes—
254C4⋊Q8—434no—
255C4⋊Q8—432no—
256#127—432no—
257#126—868no—
258#125—434no—
259#125—864no—
260#124—434no—
261#124—864no—
262#123—864no—
263#123—868no—
264C22⋊Q8—438no—
265C22⋊Q8—864no—
266C22⋊Q8—864no—
267#121—438no—
268#121—864no—
269#121—864no—
270#120—864no—
271C4×Q8—438no—
272C4×Q8—864no—
273C4×Q8—864no—
274C4×D4—438no—
275C4×D4—868no—
276C4×D4—868no—
277C4×D4—868no—
278C4×D4—864no—
279C4×D4—864no—
280#117—434no—
281#117—864no—
282#117—864no—
283#117—868no—
284C2×C42—864no—
285C2×C42D17212yes—
286C2×C42D17212yes—
287C2×C42D17212yes—
288C2×C42C22×D4314yes—
289C2×C42C22×D4311yescharacteristic
290C2×C42C22×D4311yescharacteristic
291#107—438no—
292#106—438no—
293#103—4316no—
294#102—4316no—
295#97C22×D4314yes—
296#97C22×D4314yes—
297C4×C8C22×D4318yes—
298C24C2×D17211yescharacteristic
299#41—8616no—
300#41—17216no—
301C2×Q8—434no—
302C2×Q8—864no—
303C2×D4—434no—
304C2×D4—868no—
305C2×D4—864no—
306C2×D4—864no—
307C22×C4—24no—
308C22×C4—44no—
309C22×C4—868no—
310C22×C4—864no—
311C22×C4C2×D17214yes—
312C22×C4C2×D17212yes—
313C22×C4C2×D17212yes—
314C22×C4C2×D17211yescharacteristic
315C22×C4C2×D17212yes—
316C22×C4C2×D17214yes—
317C22×C4C23×D4312yes—
318C22×C4C23×D4311yescharacteristic
319Q16—868no—
320SD16—8616no—
321D8—868no—
322M16—216no—
323C2×C8—24no—
324C2×C8#1062189818yescomplemented
325C2×C8C23×D4314yes—
326C2×C8C23×D4314yes—
327C4⋊C4—438no—
328C4⋊C4—868no—
329C4⋊C4—864no—
330C4⋊C4—864no—
331C4⋊C4—868no—
332C4⋊C4—868no—
333C22⋊C4—864no—
334C22⋊C4—868no—
335C22⋊C4—868no—
336C22⋊C4—868no—
337C22⋊C4—868no—
338C42—864no—
339C42—868no—
340C42C2×D17211yescharacteristic
341C42C2×D17214yes—
342C42C2×D17212yes—
343C42C2×D17214yes—
344C42C2×D17211yescharacteristic
345C42C23×D4312yes—
346C42C23×D4312yes—
347C23—22no—
348C23—42no—
349C23—864no—
350C23C22×D17212yes—
351C23C22×D17211yescharacteristic
352Q8—868no—
353Q8—1728no—
354D4—868no—
355D4—1728no—
356D4—17216no—
357D4—1728no—
358C2×C4—22no—
359C2×C4—28no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—868no—
366C2×C4—864no—
367C2×C4—17216no—
368C2×C4—1728no—
369C2×C4C22×D17212yes—
370C2×C4C22×D17212yes—
371C2×C4C22×D17214yes—
372C2×C4C22×D17212yes—
373C2×C4C22×D17211yescharacteristic
374C2×C4C2×#1062189814yes—
375C2×C4C24×D4311yescharacteristic
376C8—24no—
377C8C2×#1062189818yes—
378C22—22no—
379C22—24no—
380C22—22no—
381C22—44no—
382C22—1728no—
383C22—1724no—
384C22#1458344912yes—
385C22C23×D17211yescharacteristic
386C4—24no—
387C4—22no—
388C4—22no—
389C4—1728no—
390C4—1724no—
391C4#1458344912yes—
392C4#1458369914yes—
393C4C22×#1062189812yes—
394C2—22no—
395C2—42no—
396C2—3444no—
397C2C2×#1458344911yescharacteristic
398C2C2×#1458369912yes—
subgroupG/H
centerC42C2×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×M16×C43C2
socleC22×C43C23×D4
hypercenterC2×C4×M16D43
hypocenterC43#60676
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19147891C2semidirect
2. #19145201C2semidirect
3. #19145190C2semidirect
4. #19145119C2semidirect
5. #19145041C2semidirect
6. #19144941C2semidirect
7. #19144204C2semidirect
8. C4×#13063347C2semidirect
9. C2×C4×M16×C43C2semidirect
22. #14583308C22semidirect
23. #14583293C22semidirect
24. #14583288C22semidirect
25. #14583268C22semidirect
26. #14583264C22semidirect
27. #14583259C22semidirect
31. C4×Dic172C22semidirect
32. C4×#10621873C22semidirect
33. C4×D344C22semidirect
121. C2×C8×C43#41semidirect
203. C2×C4×M16D43semidirect
241. C43#60676semidirect
324. C2×C8#10621898semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191478912
#191452012
#191451902
#191451192
#191450412
#191449412
#191442042
C4×#130633472
C2×C4×M16×C432
#6067643